The factorization of generalized Fermat numbers 12^2^k + 11^2^k

 k               factorization
---   ------------------------------------
 1    5 * 53
 2    17 * 2081
 3    113 * 5702129
 4    929 * 2689 * 262369 * 352193
 5    449 * 80831997464815383957493223207873
 6    641 * 441738113 * 4142196236086054595120177167536933992184466613226792461569
 7    257 * 32257 * 183809 *    factor7
 8    562574849 *               factor8
 9    2378806273 *              factor9
10    6782977 *                 factor10
11    2540433409 *              factor11
12                              factor12    proved composite by PrimeForm.exe
13    163841 *                  factor13
14    65537 *                   factor14
15    67969155073 *             factor15
16                              factor16    proved composite by PrimeForm.exe
17    786433 *                  factor17
18                              factor18    proved composite by PrimeForm.exe
19                              factor19    proved composite by PrimeForm.exe
20    1120902578177 *           factor20
21    699274362881 *            factor21
22    167772161 *               factor22


All explicit factors are provable primes.